Home
Class 12
MATHS
If f:R-{-1}toR and f is differentiable f...

If `f:R-{-1}toR and f` is differentiable function satisfies:
`f((x)+f(y)+xf(y))=y+f(x)+yf(x)AAx,`
`yinR-{_1}` Find f(x).

Text Solution

Verified by Experts

The correct Answer is:
`f(x)=(-x)/(1+x)`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DIFFERENTIAL EQUATION

    ARIHANT MATHS|Exercise Exercise (Subjective Type Questions)|4 Videos

  • DETERMINANTS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|18 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

Similar Questions

Explore conceptually related problems

If f:R-{-1}rarr R and f is differentiable function satisfies f(x+f(y)+xf(y))=y+f(x)+y.f(x) for all x,y belongs to R-{-1} then find the value of 2010[1+f(2009)]

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

Knowledge Check

  • Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

    A
    `2 log_(e) x`
    B
    `3 log_(e) x`
    C
    `log_(e) x`
    D
    `(1)/(2)log_(e)x`

    • Similar Questions

    Explore conceptually related problems

    Let f:R rarr R be a differentiable function satisfying 2f((x+y)/(2))-f(y)=f(x) AA x , y in R ,if f(0)=5 and f'(0)=-1 , then f(1)+f(2)+f(3) equals

    If f(x) be a differentiable function,such that f(x)f(y)+2=f(x)+f(y)+f(xy);f'(0)=0,f'(1)=2 then find f(x)

    Let f be a differentiable function satisfying the relation f(xy)=xf(y)+yf(x)-2xy (where x,y>0) and f'(1)=3, then

    Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(x) AAx, y in R ^(+) also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))] (where [.] denotes greatest integer function).

    Let f :R to R be a differentiable function satisfying: f (xy) =(f(x))/(x) AAx, y in R ^(+) also f (1)=0,f '(1) =1 find lim _(x to e) [(1)/(f (x))] (where [.] denotes greatest integer function).

    f(x) is a real valued function, satisfying f(x+y)+f(x-y)=2f(x).f(y) for all yinR , Then

    Let f be a differentiable function satisfying f(x/y)=f(x)-f(y) for all x ,\ y > 0. If f^(prime)(1)=1 then find f(x)dot

    Home
    Profile